Orbifold Bergman Kernels

Let $(X,\omega )$ be a compact $n$-dimensional Kähler orbifold, the stabilizer groups of which are abelian and have rank at most two. Let $E$ be an orbi-ample vector bundle of rank $2$ over $X$ and let $H$ be a Hermitian metric on $E$ such that the curvature form of $\det H$ is $-2\pi \sqrt{-1}\omega$. We show that a certain weighted sum of Bergman kernels for ${Sym}^{i}E\otimes \det (E{)}^{k+j}$ as $i$ and $j$ vary over a finite set admit an asymptotic expansion. This extends a similar result for cyclic Kähler orbifolds.